Point processes are a very general formulation. In nature we may find specific processes exhibiting behaviour which at first glance may seemingly stem from a random distribution of arrivals, but after closer examination they may fail to be random at all. For example, if we want to understand the probability of an earthquake happening, this process exhibits non-random behavior. Instead such processes exhibit a self-exciting behavior. One arrival increases the probability of the next. The following definition describes a Hawkes processes, named after its creator to model seismic activity[1]}.
